The invention relates to machine elements and mechanisms, but more particularly, the invention relates to a toothed power transmission belt and a sprocket.
A conventional toothed belt, as described in U.S. Pat. Nos. 2,507,852 to Case and 2,934,967 to Warral, has teeth of essentially trapezoidal cross section which are similar to gear rack teeth. Another type flat-face tooth belt is shown in British Pat. No. 744,907.
Another conventional toothed belt is disclosed in U.S. Pat. No. 3,756,091 to Miller. The belt has teeth with generally round cross sections composed of two circular intersecting arcs. The belt teeth mesh with mating, conjugate, sprocket teeth. The size of the belt and sprocket teeth, radii of curvature, tooth angles, and belt tooth isochromatic and isoclinic fringe patterns are characterized by a set of rigorous design criteria and formulas.
The belts described in the Case, Warral and Miller patents each comprise a substantially inextensible tensile member with predominantly elastomeric teeth bonded to one side thereof. Optionally, a protective fabric covers the exterior surface of the teeth. The belt may also include a backing layer of an elastomeric material that is identical or similar to the material from which the teeth are constructed. Many different materials may be used to construct either belt. Some of the more common materials are neoprene or polyurethane.
While both the round tooth and trapezoidal tooth power transmission belts are recognized as viable means for positive drive power transmission, there is still need for improved power capacity in a toothed belt. Under high driving load conditions, the trapezoidal and round toothed belts have radial load problems as the mating belt and sprocket teeth slide into engagement with each other, creating undesirable wear and heat and introducing a radial force which tends to deflect and disengage the belt teeth from the sprocket. Compression stress must be carried through the belt teeth to the belt tensile member. Thus, the belt tension may, and the driving load vector does contribute to unnecessary compression strain of the elastomeric belt teeth.
In both prior art type belts, belt teeth are supported to a great extent on at least one side of successive sprocket teeth. Trapezoidal belt teeth lay on the sprocket teeth much like a V-belt wedges in a sheave. Round belt teeth are supported on their curvilinear driving surfaces by mating conjugate sprocket teeth. Consequently, the elastomeric teeth are subjected to radial compression stresses.
Radial compression stress of a belt tooth is in a direction along a radial line of a meshing sprocket. It has two sources: The first source is longitudinal belt tension, and the second source is the driving load transmitted between the belt and sprocket teeth during dynamic conditions. Belt tension would introduce radial compression strain to the belt teeth if there were no back-lash clearance between the meshing belt and sprocket teeth. Of course, when there is clearance between the belt and sprocket teeth, belt tension radially compresses the belt in the land areas between successive belt teeth.
Under operating conditions, a sprocket transmits a driving load to meshing trapezoidal belt teeth in a direction substantially perpendicular to the planar driving surfaces of the teeth. The angle is typically 20.degree.-25.degree. in relation to a perpendicular to the belt. This driving load develops a radial (compression) component and a tangential (shear) component in the belt teeth. A typical driving load applied to trapezoidal belt teeth is shown in FIG. 6. As shown in FIG. 11 of Miller, such a tooth has a region of high stress and strain at its root resulting from shear and compression loading by the driving load vector.
The round toothed belt was developed to overcome stress concentration problems associated with the trapezoidal toothed belt. The Miller patent sets forth a detailed comparison of the characteristics of each belt. For the round toothed belt, a driving load is applied along the entire curvilinear surface of the teeth by conjugate teeth of a meshing sprocket. The driving load is distributed along the entire driving surfaces of the belt teeth to effect a stress distribution where the one-half order isochromatic fringe of the elastomeric belt teeth has a shape that substantially matches the conjugate sprocket teeth. This means that the resultant driving load vector applied to the belt teeth must be at a substantially large angle in relation to a perpendicular from the belt tensile members. As shown in FIG. 5, the resultant power load vector angle may be nearly 45.degree. in relation to a perpendicular belt assuming that the belt teeth are evenly stressed across their curvilinear driving surfaces. Miller points out that the belt teeth that are in engagement with the sprocket share equally in receiving the driving load.
While a rounded toothed belt may evenly distribute stresses across its entire curvilinear driving surfaces, it nevertheless, has the same intrinsic problem as a trapezoidal toothed belt. That is, belt tension and the resultant driving load vector radially compress the belt teeth. Consequently, the belt teeth are constantly strained by a radially oriented load that does not contribute to power transmission. In other words, that effect gained by redistribution of stress within the elastomeric belt teeth may be lost as the teeth are strained by unnecessary radial load components that may especially result from use of small diameter sprockets.
A problem results as the Miller type sprockets are made smaller in diameter once a belt pitch is established (to wit, 14 millimeter). Belt pitch remains constant and is measured along its substantially inextensible tensile member. However, the arcuate interspacing between successive teeth becomes smaller as the belt is bent to smaller radii around increasingly smaller sprockets. Sprocket tooth pitch must be made correspondingly smaller. Accordingly, the sprocket tooth tip becomes so small that it becomes pointed. This is because Miller requires full support of the tooth underbody to achieve his one-half order isochromatic fringe. Since the reduction for tooth interspacing cannot come from the sprocket cavity which forms the conjugate surfaces, it must come from the sprocket tooth tip.